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A mathematical approach to desynchronization of coupled oscillators: application to a neuronal ensemble. (English) Zbl 1280.93040

Summary: Synchronization of neurons plays an important role in vision, movement and memory. However, many neurological disorders such as epilepsies, Parkinson disease and essential tremor are related to excessive synchronization of neurons. In the line of therapy, stimulations to these pathologically synchronized neurons should be capable of breaking synchrony. As the first step of designing an effective stimulation, we consider desynchronization problem of coupled limit-cycle oscillators ensemble. First, the desynchronization problem is redefined in a nonlinear output regulation framework. Then, we design an output regulator (stimulation) which forces limit-cycle oscillators to track exogenous sinusoidal references with different phases. The proposed stimulation is robust against variations of oscillators’ frequencies. Mathematical analysis and simulation results reveal the efficiency of the proposed technique.

MSC:

93C10 Nonlinear systems in control theory
92C20 Neural biology
93C95 Application models in control theory
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